In a small bowl, whisk together vinegar, oil, basil, oregano, garlic, salt, and pepper.

Pour over the mushrooms.

Let stand at room temperature for 15 minutes or so, turning twice.

Light your Black Knight barbecue and brush grill with oil.

Place mushrooms on the grill, reserving marinade for basting.Grill for 5 to 8 minutes on each side, or until tender. Brush with marinade frequently. Top with cheese during the last 2 minutes of grilling.